High school science courses identified in 19 TAC, Chapter 112 (http://ritter.tea.state.tx.us/rules/tac/. High school technology application courses identified in 19 TAC, Chapter 126 (http://ritter. tea.state.tx .us/rules/.
Probability
Statistical models are very useful because they can describe the probability or probability of an event and provide alternative outcomes if the event does not occur. However, they often use statistical models to tell you how likely it is to rain at any given time, and you can prepare yourself based on this probability.
Key Terms
The parameter is the proportion of medical doctors who have been involved in one or more malpractices in the population. The statistic is the proportion of medical doctors who were involved in one or more malpractices in the sample.
1.2 | Data, Sampling, and Variation in Data and Sampling
Find a population, a sample, the parameter, the statistic, a variable, and data for the following study: You want to determine the average—mean—number of glasses of milk college students drink per day. Suppose you asked five students in your English class yesterday how many glasses of milk they drank the previous day.
Introduction
A possible solution
The weights of the soup (19 oz, 14.1 oz, 19 oz) are quantitative continuous data because you are measuring weights as precisely as possible. Items a, d and g are quantitatively discrete; items c, f and h are quantitatively continuous; items b and e are qualitative or categorical.
Qualitative Data Discussion
In the graph, the percentages add up to more than 100 percent, because students can fall into more than one category. The following pie charts include the Other/Unknown category because the percentages must add up to 100 percent.
Marginal Distributions in Two-Way Tables
Note - The term marginal distribution gets its name from the fact that the distributions are located at the edges of frequency distribution tables. In other words, the reason that 20 is the cutoff frequency in this two-way table is because it represents the edge or fraction of the total population that is female (20/50).
Conditional Distributions in Two-Way Tables
The entries in the total row and total column represent marginal frequencies or marginal distributions. Marginal distributions require bivariate data and focus on only one of the variables shown in the table.
Presenting Data
For each graph, explain which features they should point to and the potential display problems that may exist. For the pie chart, have them point out which color represents part-time students and which one represents full-time students.
Sampling
Then use simple random sampling to choose proportional numbers of students from the first year and do the same for each of the remaining years. To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters.
Critical Evaluation
This table displays six sets of quiz scores (each quiz counts 10 points) for an elementary statistics class. Continue counting ten quiz scores and recording the quiz score until you have a sample of 12 quiz scores.
Variation in Data
Twenty-four people said they would like more talk shows, and 176 people said they would like more music. Do you think this sample is representative of (or characteristic of) the entire population of 20,000 listeners?
Variation in Samples
The station uses convenience sampling and surveys the first 200 people they meet at one of the station's music concert events. The statistician's job is to see through the variability and draw appropriate conclusions.
Answers and Rounding Off
Once you have a set of data, you need to organize it so that you can analyze how often each datum occurs in the set. However, when calculating the frequency, you may need to round your answers to be as precise as possible.
Levels of Measurement
Especially in Probability Topics, the chapter on probability, it is more useful to leave an answer as an unreduced fraction.
Frequency
Have someone in your class conduct a survey on the number of siblings (siblings) each student has.
1.4 | Experimental Design and Ethics
When participation in a study elicits a physical response from a participant, it is difficult to isolate the effects of the explanatory variable. The explanatory variable is scent and the response variable is the time taken to complete the maze.
Ethics
Even if the answers she uses are actual answers provided by other participants, the duplication is deceptive and can create bias in the data. Only two types of juice were included in the study: apple juice and cranberry juice.
1.5 | Data Collection Experiment
Data Collection Experiment
Student Learning Outcomes
Movie Survey
Order the Data
Discussion Questions
1.6 | Sampling Experiment
Sampling Experiment
Restaurants Stratified by City and Entree Cost
A Simple Random Sample
A Systematic Sample
A Stratified Sample
A Cluster Sample
KEY TERMS
Choose every kth person in the list, starting with the one selected at random.
CHAPTER REVIEW
It is important to learn basic statistical procedures in order to know the proper analysis of data.
PRACTICE
27. Would the sample size be large enough if the population is school students. 35. The company takes the two studies as proof that their software causes mental improvement in stroke patients.
HOMEWORK
What share of people surveyed have lived in the United States for five or seven years? What share of people surveyed have lived in the United States for at most 12 years?
BRINGING IT TOGETHER: HOMEWORK
Students must be able to get textbooks right at the beginning of the academic term. Write an analysis of his study that addresses the following questions: Is his sample representative of the population of all college textbooks.
He decides to examine one textbook for each of the following seven subjects: calculus, biology, chemistry, physics, statistics, geology, and general engineering. Describe some possible sources of bias in this study, and how they may affect the results of the study.
SOLUTIONS
If a large number of people refuse to participate, the sample may not have the same characteristics as the population. He also only looked at the most popular textbook for each of the topics he researched.
2 | DESCRIPTIVE STATISTICS
From this data, calculate the conditional distributions for the subpopulation of men who own each pet type.
2.2 | Histograms, Frequency Polygons, and Time Series
The following data is the number of books purchased by 50 part-time students at ABC College. The following histogram shows the number of books on the x-axis and the frequency on the d-axis.
Frequency Polygons
One feature of the data that we might want to consider is that of time. Since each date is paired with the temperature reading for the day, we don't have to think about the data being random.
Constructing a Time Series Graph
A graph that recognizes this order and shows the changing temperature as the month progresses is called a time series graph. Use the table to construct a time series graph of CO2 emissions for the United States.
2.3 | Measures of the Location of the Data
Thus, the median of the lower half, or first quartile (Q1), will be the middle value, or 2. This equation tells us the sei, or position of the data value in the data set, is 21.
A Formula for Finding the Percentile of a Value in a Data Set
Interpreting Percentiles, Quartiles, and Median
The first quartile is the median of the lower half of the scores and does not include the median. The third quartile is the median of the top half of the scores and does not include the median.
2.4 | Box Plots
The first data set has the widest spread for the middle 50 percent of the data. Construct a box plot using a graphing calculator for each set of data and indicate which box plot has the widest spread for the middle 50 percent of the data.
2.5 | Measures of the Center of the Data
As discussed earlier, if it is an odd number, the median is the middle value of the ordered data (arranged from smallest to largest). The following example illustrates the location of the median and the value of the median.
The Law of Large Numbers and the Mean
The mod may show that most people lose two pounds in the first week, making the program less appealing. For example, if the data set is red, red, red, green, green, yellow, purple, black, blue, the mode is red.
Sampling Distributions and Statistic of a Sampling Distribution
Consider a weight loss program that advertises an average weight loss of six pounds in the first week of the program.
Calculating the Mean of Grouped Frequency Tables
What is the best estimate for the average number of hours spent playing video games.
2.6 | Skewness and the Mean, Median, and Mode
In summary, in general, if the data distribution is skewed to the left, the mean is less than the median, which is often less than the mode. If the data distribution is skewed to the right, the mode is often less than the median, which is less than the mean.
2.7 | Measures of the Spread of the Data
The standard deviation
The lowercase letters represent the sample standard deviation and the Greek letterσ(lowercase) represents the population standard deviation. The lowercase letters represent the sample standard deviation and the Greek letterσ (lowercase sigma) represents the population standard deviation.
Types of Variability in Samples
The symbol σ2 represents the population variance; the population standard deviationσ is the square root of the population variance. The symbols 2 represent the sample variance; the sample standard deviations are the square root of the sample variance.
Sampling Variability of a Statistic
The long left side of the box plot is reflected on the left side of the histogram. The box plot also tells us that the lowest 25 percent of exam scores are D's and F's.
Standard deviation of Grouped Frequency Tables
Comparing Values from Different Data Sets
The following lists provide a few facts that give a little more insight into what the standard deviation tells us about the distribution of the data. It is important to note that this rule only applies when the shape of the distribution of the data is bell-shaped and symmetrical; we will learn more about this when we study the normal or Gaussian probability distribution in later chapters.
2.8 | Descriptive Statistics
Descriptive Statistics
Collect the Data
Analyze the Data
65.Which is the largest, the mean, mode, or median of the data set. 66.What is the minimum, mean, mode, and median of the data set.
3 | PROBABILITY TOPICS
How likely is it that a randomly selected person from your class has change in their pocket? How likely is it that a randomly selected person from your class has ridden the bus in the past month?
3.1 | Terminology
To calculate the probability of an event If all outcomes in the sample space are equally likely, count the number of outcomes for event and divide by the total number of outcomes in the sample space. If you were to roll the die a very large number of times, you would expect, in general, 2.
3.2 | Independent and Mutually Exclusive Events
Independent Events
When James draws a marble from the bag for the second time, the chance that he draws blue is still 4. You put this card aside and choose the second card from the 51 cards still in the deck.
Mutually Exclusive Events
